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Fibre (rod) and sheet-shaped crystals with specified size for use
as final products without additional machining are required in
various applications of modern engineering. In order to avoid
formation of internal mechanical stress in the crystal, lateral
surface shaping without contact with container walls is preferred.
As the crystal is not restricted by crucible walls, its
cross-section is determined by the meniscus-shaping capillary
forces and the heat and mass-exchange in the melt-crystal system.
Any variation of the pulling rate, pressure, temperature gradient
in the furnace, and melt temperature at the meniscus base leads to
a change in the crystal cross-section and to pinch formation. Over
the past two decades, many experimental and theoretical studies
have been reported on a powerful approach to crystal lateral
surface shaping without contact with container walls, namely the
so-called edge-defined film-fed growth (EFG) technique. The shape
and size of a single crystal grown by EFG is determined by the
shape and size of the meniscus, (i.e: the liquid bridge retained
between the die and the crystal) which depend on the radius or
half-thickness of the die and other properties such as pulling
rate, pressure, temperature gradient and melt temperature. In this
book, theoretical and numerical results are obtained using a
non-linear mathematical model of the EFG method. Theoretical
results presented for fibres and sheets are rigorously obtained on
the basis of the equations of the model. Numerical results are
obtained on the basis of theoretical results using experimental
data. Such results offer a complete package of the possibilities of
the model for equipment designers and practical crystal growers.
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